A) \[{{b}^{2}}+{{c}^{2}}\]
B) \[{{b}^{2}}-{{c}^{2}}\]
C) \[\frac{1}{b}+\frac{1}{c}\]
D) \[\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}\]
Correct Answer: B
Solution :
\[a(b\cos C-c\cos B)\] \[=ab\cos C-ac\cos B\] \[=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2}-\frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2}\] \[={{b}^{2}}-{{c}^{2}}\]
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